Question

A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time is shown in the following table

Weight (kg)	2	4	5	8
Length (cm)	3	4	4.5	6

Find the equation relating the length of the spring to the weight on it

Answer 1

The points are(2, 3), (4, 4), (5, 4.5), (8, 6)

The relation connecting weight and Length is the equation of the straight line joining the points (2, 3) and (4, 4)

`(x - 2)/(4 - 2) = (y - 3)/(4 - 3)`

`(x - 2)/2 = (y - 3)/1`

x – 2 = 2(y – 3)

x – 2 = 2y – 6

x – 2y + 6 – 2 = 0

x – 2y + 4 = 0 .......(1)

which the required relation connecting weight and length.